Fractal mathematics in managed care? How a simple and revealing analysis could improve the forecasting and management of medical costs and events.

Abstract

In 1995, Christopher Barton, a research geologist who had worked for a decade with mathematician Benoit Mandelbrot, met with a group of U.S. research scientists interested in improving methods of forecasting hurricane wind speed at landfall and consequent damage. Noting that most hurricanes were small and of little consequence, while a few produced catastrophic damage, the group sought a more accurate way to forecast cataclysmic wind events. In response, Barton used U.S. historical data documenting maximum wind speeds for each hurricane at landfall dating from the year 1900 to create a cumulative frequency distribution (CFD) for wind speed, that is, the total number of hurricanes that had attained a given landfall wind speed for locations along the U.S. coast from Maine to Mexico. He then plotted the base 10 logarithms (log10) of CFD versus wind speed for each location. The resulting plot revealed a striking pattern of 2 separate mathematical functions. Noting that the wind speed where the 2 slopes intersected was approximately 40-50 meters per second (m/s), or about 90-110 miles per hour, Barton asked a group of research meteorologists at the National Oceanic and Atmospheric Administration’s National Hurricane Research Center if there was any meteorological significance to a 40 m/s wind speed. The startled meteorologists replied that approximately 40 m/s signals the formation of the hurricane’s eyewall and the transition from one physical process to another.1,2 In less than 15 years since that meeting, a growing number of forecasters and researchers—including meteorologists, geophysicists, and biologists—have applied similar mathematical approaches to the measurement and forecasting of a broad range of natural physical phenomena. 3-7 When plotted on log-log scales, data representing the magnitude versus number of many natural phenomena often reveal much the same mathematical pattern as did the hurricane wind speeds plotted by Barton and his colleagues. Specifically, these data exhibit “power law” (fractal) scaling. In this editorial, we explain fractal scaling, highlight current health care trends that could make the use of fractal mathematical analysis increasingly important for the managed care industry, present a sample analysis from the physical sciences, and propose potential uses of the technique. We begin with 2 key concepts of fractal mathematics that apply across multiple venues